Gemara

(Beraisa) Suggestion: Perhaps "mi'Yom ha'Rishon Ad Yom ha'Shevi'i" (one who eats Chametz from the first day of Pesach until the seventh gets Kares) does not apply to days one and seven!

We find that a Metzora becomes Tahor if the Tzara'as spreads "mi'Rosho v'Ad Raglav", and this does not include the head or the legs.

Rejection: "Ad Yom ha'Echad v'Esrim la'Chodesh ba'Arev" (includes the seventh day. "Ba'Erev Tochlu Matzos" includes the first day.).

Rebbi says, we need not learn from another verse. Yom Rishon and Yom ha'Shevi'i are included (because it says "Ad").

Berachos 9b (Mishnah - R. Eliezer): The time for the morning Shma lasts until sunrise;

R. Yehoshua says, it extends until the third hour of the day, for this is when kings rise.

3b (Beraisa - Rebbi): There are four Mishmaros in the night;

R. Nasan says, there are three.

(R. Zerika): Rebbi learns from "Chatzos Lailah Akum" and "Kidmu Einai Ashmuros." (David would rise at midnight; this was "Ashmuros" (plural) before morning);

Since there are two Mishmaros in half the night, there are four in all.

R. Nasan holds like R. Yehoshua (who permits Shma until three hours, which is when kings rise. There are three Mishmaros. Each is four hours.)

David said that he rises eight hours (six of the night and two of the day) before other kings, i.e. two Mishmaros.

(Rav Ashi): (R. Nasan need not hold like R. Yehoshua. David says that he rises six hours before morning.) The plural "Ashmuros" can refer to one and a half Mishmaros.

10b (Mishnah - Beis Shamai): In the morning, one stands to say Shma, for it says "uv'Kumecha";

Beis Hillel says, one recites in whatever position he is -- "uv'Lechtecha va'Derech." "Uv'Kumecha" teaches that we recite at the time that (most) people rise.

Beis Shamai: If the verse intends to teach about the time for Shma, it should have said "uva'Boker"! Rather, "uv'Kumecha" means when you actually rise.

Pesachim 107b (Beraisa): On Erev Pesach, even Melech Agripas, who normally ate (began his first meal) during the ninth hour, may not eat until dark.

One might have thought that nine hours for Agripas is like four hours (the meal time) for common people (i.e. he may eat then, and he will be able to eat Matzah at night with appetite). The Beraisa teaches that this is not so.

Avodah Zarah 4b: Hash-m's fury is a moment;

(Abaye): It is in the first three hours of the day, when a rooster's mane turns (totally) white.

(Beraisa - R. Meir): When the sun shines and kings put on their crowns and bow to the sun, immediately Hash-m gets angry.

(Rav Yosef): An individual should not pray Musaf during the first three hours of the day on Rosh Hashanah. Since Hash-m judges then, perhaps He will scrutinize his deeds, and his prayer will be rejected.

Ta'anis 25b (Beraisa - R. Yosi): If they were fasting and rain came, the finish the fast only if this was after nine hours. We find that Achav Melech Yisrael fasted after nine hours.

Rishonim

Rambam (Hilchos Kri'as Shma 1:11): The Mitzvah is to read Kri'as Shma before sunrise, so he finishes reading and says the Berachah afterwards at sunrise. If he delayed and read afterwards, he was Yotzei, for the time is until the end of three hours for one who transgressed and delayed.

Hagahos Maimoniyos (9): The Re'em (Yere'im) and R. Simchah say that the time is until the third hour, i.e. the beginning of the third hour. We say that R. Noson holds like R. Yehoshua. David was eight hours earlier than other kings, i.e. six hours of the night and two of the day. Tosfos, Bahag and my Rebbi did not clarify this. They wrote Stam three hours. There is no proof from R. Noson. R. Yehoshua says until three hours, i.e. the end of three hours, for this is when kings rise. The Gemara mentioned only two hours of the day because it explained the plural Mishmaros. There was no need to mention the third hour. David counted only full Mishmaros. We find that kings slept 'until three hours'. If it meant until the beginning of the third hour, i.e. the end of the second hour, it should have said so in some place, for that is the primary way to say it. In any case it should have said 'until the third hour' to denote the beginning of the third hour. 'Three hours' connotes three full hours. The Yerushalmi connotes like this. It says that in the days of R. Yochanan they used to go to (the public Tefilah on) a Ta'anis and recite Kri'as Shma after three hours, and they did not protest. Rav Acha wanted to protest when a Tzibur read after three hours. R. Yosi told him that they already recited in its time, and they repeat it now to enter Shemoneh Esre amidst Divrei Torah. I.e. the time expires at the end of three hours. Do not say that 'after three hours' means after the beginning of the third hour. I later found that Semag says that it is until the end of three hours. He learns from another Yerushalmi, which (says that R. Berachyah said Kri'as Shma after three hours, and) asked from a Beraisa about one who recites after the time. Kings rise in (after) two hours and read in the third hour. Tosfos says similarly. He learns from the Gemara (Avodah Zarah 4b) about when Hash-m gets angry. My Rebbi agreed to all of this.

Yere'im )252 (in old printing, 13) DH Yesh): R. Yehudah says that the time is until the third hour, i.e. the beginning of the third hour. The third hour is not included. This is clear from Kesuvos "Pei Tes" (Daf 89, or perhaps Perek 9).

Roke'ach (320): The time is until the end of three hours, like it connotes in Berachos regarding Mishmaros.

To'afos Re'em (7): I do not see any source in Kesuvos. The Roke'ach (the Talmid of the Re'em) learns from Berachos 3b. Also Semag (who often cites the Re'em, Aseh 18) learns from there. It is Ad three hours, but not Ad biChlal (until and including). Our text of the Yerushalmi, and the Roke'ach's (321), says that R. Berachyah said Kri'as Shma in the third hour, and the Gemara said that this is after the time! Regarding the Ta'anis, we can say that the Gemara recorded what happened, but even if they said it during the third hour, it would have asked and answered similarly.

Rashi (Berachos 3b DH v'Tartei): David rose eight hours earlier than other kings, who sleep (at night and) two hours into the day.

Tosfos (Avodah Zarah 4b DH bi'Tlas): Hash-m's anger is in the third hour, when the sun shines and kings put on their crowns. Kings rise in three hours, like it says in Berachos.

Rashi (Ta'anis 25b DH she'Chen): From nine hours and onwards, the fast affects everyone, even princes who eat at nine hours. Until three hours they sleep, and they delay six hours and eat, like it says in Pesachim that Agripas ate at nine hours.

Eliyahu Rabah (OC 58:2): This proves that kings sleep until the end of three hours. Why did others need to bring a proof from the Yerushalmi?

Question (Tosfos Pesachim 107b DH she'Hayah): If Agripas rose at three hours, and ate in the sixth hour after rising, like Chachamim, the Gemara should have said that nine hours for Agripas is like six hours for Chachamim!

Poskim

Shulchan Aruch (OC 58:1): The time for Kri'as Shma in the morning extends until the end of three hours, which is a quarter of the day.

Beis Yosef (DH u'Mah): R. Simchah says that it is the beginning of the third hour, but Hagahos Maimoniyos rejected this. The Yerushalmi proves that it is the end of three hours. Also Tosfos (Avodah Zarah 4b), Maharam , Semag and the Rambam say so.

Bach (2): Even though kings rise at the end of two hours of the day, they delay an hour getting dressed and attending to their needs, and then they recite Shma.

Sha'agas Aryeh (5): We should say that 'until three hours' is Ad v'Lo Ad biChlal (excludes the third hour), just like the first Tana says 'Ad ha'Netz, i.e. before, but not during the sunrise! However, in the Mishnah 26b, Chachamim say that Minchah is Ad Erev (v'Lo Ad biChlal), and R. Yehudah says Ad Plag ha'Minchah, and the Gemara was unsure whether R. Yehudah means Ad biChlal. Also, we say that perhaps the first Tana holds like Vatikin, and permits during the Netz. If kings bow at three hours, they must rise during (before the end of) the third hour! However, perhaps they rise and bow at the end of three hours, and due to this, judgment is harsh the entire third hour. However, the Gemara says that kings bow when the sun shines, i.e. Netz, which is during the second hour of the day (starting from dawn)! Rather, Stam kings sleep until three hours. Those who bow to the sun rise earlier. Why did Tosfos say that one should not pray during the third hour? The Gemara connotes that one should not pray at any time during the first three hours!

Sha'agas Aryeh: Berachos 10b proves that the time is until the end of three hours. Beis Shamai said that if the verse came to teach about the time to say Shma, it would have said "uva'Boker." This connotes until four hours or until midday, according to R. Yehudah and Chachamim (who argue about the latest time for Shacharis - 26a)! Rather, Beis Shamai mean that it would have said "ba'Boker ba'Boker", to teach that it is earlier than this (the first half of the morning - 27a). They must hold like R. Yehoshua, that the time is until three hours. This shows that it is the end of three hours (half the morning).

Sha'agas Aryeh: Even though Nochri kings rise at the end of three hours, David's Chasidus was to rise eight hours earlier than Yisrael kings, who cannot sleep until the end of three hours, for they must read Kri'as Shma. This is Rashi's intent.

Gra (DH Sof): The Rambam, Hagahos Maimoniyos and other Meforshim say that 'three hours' refers to three full hours. If not, it should have said 'until the third hour.' On 7a, we say that the first three hours (Hash-m judges...)

Damesek Eliezer: His proof is from the continuation, 'the sun shines and kings put on their crowns and bow to it.' This is at the end of three hours, which is when the sun shines, like it says on 27a. (Note - the Gemara there says that this is when it is hot in the sun, but not in the shade.) This shows that kings rise at the end of three hours.

Gra: This is unlike the Re'em and Rashi, who say until the beginning of the third hour. They learn from Berachos 3b. See Tosfos Avodah Zarah 4b. This rejects their proof.

Damesek Eliezer: The text of the Gra should say 'see the Re'em and R. Simchah.' Tosfos says that different kings rise at different times during the third hour; Kri'as Shma extends until all of them are awake. David rose eight hours before the earliest of the other kings.

Mishnah Berurah (4): The Magen Avraham counts the three hours from dawn. The Gra counts them from Netz. L'Chatchilah there is no difference, for one may not delay until the end of the time.